Open Access
June 2000 Trigonal modular curves $X_0^*(N)$
Yuji Hasegawa, Mahoro Shimura
Proc. Japan Acad. Ser. A Math. Sci. 76(6): 83-86 (June 2000). DOI: 10.3792/pjaa.76.83


For a positive integer $N$, let $X_0^*(N)$ denote the quotient curve of $X_0(N)$ by the Atkin-Lehmer involutions. In this paper, we determine the trigonality of $X_0^*(N)$ for all $N$. It turns out that there are seven values of $N$ for which $X_0^*(N)$ is a non-trivial trigonal curve.


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Yuji Hasegawa. Mahoro Shimura. "Trigonal modular curves $X_0^*(N)$." Proc. Japan Acad. Ser. A Math. Sci. 76 (6) 83 - 86, June 2000.


Published: June 2000
First available in Project Euclid: 23 May 2006

zbMATH: 0973.11064
MathSciNet: MR1769974
Digital Object Identifier: 10.3792/pjaa.76.83

Primary: 11F11
Secondary: 11F03 , 11G30 , 14E20 , 14H25

Keywords: Atkin-Lehmer involution , modular curve , trigonal curve

Rights: Copyright © 2000 The Japan Academy

Vol.76 • No. 6 • June 2000
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